When looking back on the Alternative Rock Heroes Class of 1991, you’d have gotten long odds in Vegas that the Red Hot Chili Peppers would even still be together in 20 years, let alone be (arguably) the most successful band of the bunch.

Think about it and add up all the reasons the Chili Peppers should have gone down in a flaming heap any number of times.

Lead singer Anthony Kiedis went through multiple bouts of heroin addiction.

Bass player Flea, an under-the-radar quasi-genius type, also seemed like the type who’d show up in the news for decamping for five years to a remote village in Paraguay to do relief work.

The band’s guitarist position has been less stable than the seat behind Spinal Tap’s drum kit, nearly to the point of comedy. Current guitarist Josh Klinghoffer — a name I totally could’ve made up out of thin air, but didn’t — appears to be the band’s eighth.

Note: Type “how many guitarists” into a Google search box and one of the first auto-complete options is “have the Red Hot Chili Peppers had?”

What all this adds up to is a pretty hard-to-fathom ascent to near the top of the music world and a place for the Chili Peppers as one of a small handful of modern rock bands who can reliably sell out arenas and top a major music festival like Austin City Limits, which is what they’ll do Sunday.

In figures reported by Venues Today trade magazine, the Chili Peppers are one of the most consistently high-grossing live music acts of the past year, pulling in between $800,000 and $2 million per show with no other rock band not named U2 coming close.

“They have a few keys to their success, and one of them is a huge catalog of hits,” said Dave Brooks, managing editor of Venues Today. “They continue to release new stuff and do well commercially, but their back catalog from ‘Blood Sugar Sex Magik’ forward is what makes them a ‘can’t lose’ as a live draw.”

Helping the band’s case as a continued live act: There aren’t many other bands who don’t qualify for Social Security that can pretty much guarantee a gate of more than 10,000 people night after night.

In a story this year about the current crop of rock headliners, Brooks put the Chili Peppers at the front of a class that included Radiohead, Pearl Jam, Coldplay, the (now on hiatus) Foo Fighters and fellow ACL headliners the Black Keys, along with long-established acts like Bruce Springsteen, Aerosmith and Van Halen.

“Coldplay will definitely get to that level if they keep on going the way they have, and Muse can easily headline a U.S. festival or a stadium in the U.K., but the Chili Peppers just keep adding fans through modern rock radio play,” Brooks said.

As evidence, the Chili Peppers are the most-played artist at Austin alternative radio station 101X, with 16 songs in rotation racking up 67 spins in one recent week, according to program director Lynn Barstow.

“They’re broad enough that they cross over to the college girl who thinks Anthony Kiedis is a hot sex symbol and to the music snob who can get into the work that Flea does with Thom Yorke and Damon Albarn,” Barstow said. “It’s easy to just cast them in that party rock vibe, and the haters will say that Anthony can’t really carry a tune, but they can give you a two-and-a-half hour parade of hits.”

The festival’s schedule calls for the Chili Peppers to get just under two hours when they take the stage, and their performance in Chicago at this year’s Lollapalooza (under the umbrella of ACL promoter C3 Presents) suggests they’ll prove themselves worthy of that billing.

“People want to see rock stars, and when you get them up on stage, you’re seeing pros,” said Huston Powell, a partner for C3 who has booked Lollapalooza since the festival’s resurrection in 2005.

“When we booked them as headliners in 2006, that was a real turning point for bringing the festival back, because they were the first real big arena-level act that committed and gave it some real legitimacy,” he said. “I’m as surprised as anyone at the huge way the younger generation likes the Chili Peppers, but I saw it in Chicago, and all you can say is they have classic songs that still get played, and people like to hear them a lot.”